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(a^2+1)/(2b^2-3)=(a-1)/(2b-1) diophantine

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2013 p1

February 13, 2020

number theoryDiophantine equationdiophantine

Problem Statement

Find all pairs of integers

a, b

for which equality holds

\frac{a^2+1}{2b^2-3}=\frac{a-1}{2b-1}